Scorecard models are effective tools for providing scores that characterize a particular data set for predictive purposes (e.g., to determine a likelihood of a future event taking place). The most common prediction tasks for scorecards are to estimate a function ƒ from predictors to a target domain. In contrast to scorecard models, a linear regression model is a linear combination of predictors:
      f    =                  w        0            +                        ∑                      i            =            1                    I                ⁢                              w            i                    ⁢                      x            i                                ,
where xi is the value of the ith predictor, and wi the regression weight to be trained.
Compared with regression models, scorecard models can have a binning step to divide each predictor space into bins that are then assigned weights.
      f    =                  w        0            +                        ∑                      i            =            1                    I                ⁢                              f            i                    ⁡                      (                          x              i                        )                                ,
where ƒi(xi) is the predictor score:
                    f        i            ⁡              (                  x          i                )              =                  ∑                  j          =          1                          J          i                    ⁢                        w          ij                ⁢                              b            ij                    ⁡                      (                          x              i                        )                                                  b        ij            ⁡              (                  x          i                )              =          {                                    1                                              if              ⁢                                                          ⁢              value              ⁢                                                          ⁢              of              ⁢                                                          ⁢                              x                i                            ⁢                                                          ⁢              belongs              ⁢                                                          ⁢              to              ⁢                                                          ⁢              the              ⁢                                                          ⁢                              j                ⁢                th                            ⁢                                                          ⁢              bin                                                            0                                else                              
wij: the score weights associated with bin j for predictor xi.
bij: the indicator of variables for the bins of predictor xi.
Bins for all predictors can be generated using various binning algorithms which can also support categorical predictors. Missing values can be handled by using a missing value bin. Given enough bins for a predictor xi, the above predictor score function ƒi(xi) is flexible to approximate any general function based on a single predictor, and the scorecard model is the sum of such functions. The complete, compact representation of a model by its bin definitions and weights makes the scorecard a popular, transparent, and easily understood model formulation. And the ability of a scorecard to approximate general functions makes it a strong predictive tool.
Scorecards can be trained to optimize the bin weights such that the prediction errors of the model are minimized. Scorecards can be used to predict both continuous and binary targets. For continuous targets, the error function is usually a root mean square error (RMSE) function. For binary targets, common objective functions include maximizing Kullback-Leibler divergence or Bernoulli likelihood can be used.
Scorecards are much more powerful than regression models, and still simple enough to be interpretable. By looking into the bin weights for the predictors, insight can be gained for the data.